Constructive Approximation

, Volume 34, Issue 3, pp 371–391 | Cite as

Regularity of Tensor Product Approximations to Square Integrable Functions

Article

Abstract

We investigate first-order conditions for canonical and optimal subspace (Tucker format) tensor product approximations to square integrable functions. They reveal that the best approximation and all of its factors have the same smoothness as the approximated function itself. This is not obvious, since the approximation is performed in L2.

Keywords

Tensor products Low-rank approximation Optimal subspace approximation Sobolev spaces 

Mathematics Subject Classification (2000)

15A69 41A46 49N60 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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